text: In reality water molecule dissociation (the splitting into HO and OH ions) occurs only at the electrode region (because of the ions continuously consumed at the two electrodes); however it effectively appears that the molecules split in the middle of the gap, with HO ions migrating towards the cathode and OH ions migrating towards the anode, respectively. The assistance of the huge electric field in the nano-gap (see section "Electric field distribution") not only increases the transport rate but also the water molecules ionization has been enhanced (i.e.' local concentration has been enhanced). Looking from a microscopic perspective, the total effect appears like the breakdown of water molecules.
  However this effect is not traditional breakdown, which in fact requires a much larger electric field around 1 V/Å. In the nanogap cells the huge electric field is still not large enough to split water molecules directly. However it can take advantage of the self-ionization of water, facilitating the equilibrium reaction to shift in the ionization direction.
  Such field-assisted ionization, with the fast ion transport (mainly migration), performs very in a similar way to the breakdown of water molecules; that is why this field-assisted effect is named the "virtual breakdown mechanism".
  Consider the equation of conductivity,
  Here the ion charges are not changed. The ion concentration is enhanced but only contributes to the conductivity partially. The fundamental change here is that "apparent mobility" has been significantly enhanced, as the "breakdown" effect. (In traditional electrochemical cells, although the ion intrinsic mobility is high, since there is nearly zero electric field inside bulk solution, it cannot contribute to the conductivity.) Consider the equivalent resistance between the two electrodes, as given by:
  When we decrease the gap distance between the two electrodes, not only does the value of L decrease but also the value of resistivity decreases as well; this in fact contributes more to the decrease of the total resistance.
  This "virtual breakdown mechanism" can be applied to almost all kinds of weakly-ionized materials; in fact, such weaker ionization can lead to larger Debye-length inside the solution. At the same size scale it actually helps to achieve the virtual breakdown effect.